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Simplifying -6n2 + -1n + 6 = 0 Reorder the terms: 6 + -1n + -6n2 = 0 Solving 6 + -1n + -6n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1 + 0.1666666667n + n2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.1666666667n + 1 + n2 = 0 + 1 Reorder the terms: -1 + 1 + 0.1666666667n + n2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.1666666667n + n2 = 0 + 1 0.1666666667n + n2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.1666666667n + n2 = 1 The n term is 0.1666666667n. Take half its coefficient (0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. 0.1666666667n + 0.006944444447 + n2 = 1 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667n + n2 = 1 + 0.006944444447 Combine like terms: 1 + 0.006944444447 = 1.006944444447 0.006944444447 + 0.1666666667n + n2 = 1.006944444447 Factor a perfect square on the left side: (n + 0.08333333335)(n + 0.08333333335) = 1.006944444447 Calculate the square root of the right side: 1.003466215 Break this problem into two subproblems by setting (n + 0.08333333335) equal to 1.003466215 and -1.003466215.Subproblem 1
n + 0.08333333335 = 1.003466215 Simplifying n + 0.08333333335 = 1.003466215 Reorder the terms: 0.08333333335 + n = 1.003466215 Solving 0.08333333335 + n = 1.003466215 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + n = 1.003466215 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + n = 1.003466215 + -0.08333333335 n = 1.003466215 + -0.08333333335 Combine like terms: 1.003466215 + -0.08333333335 = 0.92013288165 n = 0.92013288165 Simplifying n = 0.92013288165Subproblem 2
n + 0.08333333335 = -1.003466215 Simplifying n + 0.08333333335 = -1.003466215 Reorder the terms: 0.08333333335 + n = -1.003466215 Solving 0.08333333335 + n = -1.003466215 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + n = -1.003466215 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + n = -1.003466215 + -0.08333333335 n = -1.003466215 + -0.08333333335 Combine like terms: -1.003466215 + -0.08333333335 = -1.08679954835 n = -1.08679954835 Simplifying n = -1.08679954835Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.92013288165, -1.08679954835}
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